Free Printable ANT-IAT-II(MCQ)

1.

For polynomials in $F\left[x\right]$ every non-zero polynomial of ---- is irreducible.

a)

a) degree $\ge$ 1

b)

b) degree $\le$ 1

c)

c) degree $\ge$ 2

2.

A polynomial $f\left(x\right)\in F\left[x\right]$ having its leading co-efficient 1 is called ----

a)

a) Monic

b)

b) Field

c)

c) Ideal

3.

How many monic polynomials in $Z_7\left[x\right]$ have degree 5 ?

a)

a) 7

b)

b) $7^6$

c)

c) $7^5$

4.

Is $S\left(x\right)=x^2+1$ is reducible in $Z_2\left[x\right]$

a)

a) Yes

b)

b)No

5.

If $\left|F\right|=q$ and degree $s\left(x\right)=n\ ,$ then $\frac{\text{F[x]}}{\text{s(x)}}$ contains …….. elements.

a)

a) $n^q$

b)

b) $q^n$

c)

c)Not defined

6.

The Division Algorithm is contains ---- parts.

a)

a)Two

b)

b) Three

c)

c)Infinite

7.

Find the quotient and remainder when the first integer is divided by the second (207, 15)

a)

a) q = -1, r = 2

b)

b) q = 13, r = 12

c)

c)q = 11, r = 15

8.

Find the positive factor of f(19)

a)

a) {1, 3, 19}

b)

b) {1, 19)

c)

c) {1, 3, 7, 19}

9.

25 div 5 = ---

a)

a) 0

b)

b) 5

c)

c) 1

10.

Every non empty set of positive integers has a least number.

a)

a) The well ordering principle

b)

b) The pigeonhole principle

c)

c) The inclusion-Exclusion principle

11.

Let f(n) denote the number of positive factors of a positive integer n, Evaluate f(12)

a)

a) 6

b)

b) 4

c)

c) 2

12.

Evaluvate $\sum_{\text{d / 18}}^{ }\left(\frac{\text{1}}{\text{d}}\right)$ where d is a positive integer.

a)

a) $\frac{\text{33}}{\text{18}}$

b)

b) $\frac{\text{39}}{\text{18}}$

c)

c) 39

13.

The sum of any two odd integers is ---

a)

a) Odd

b)

b) Even

c)

c) Neither odd nor even

14.

The sum and the product of any two even integers are ---

a)

a) Even

b)

b) Odd

c)

c) None of these

15.

The product of any two odd integer is ---.

a)

a) Even

b)

b) Odd

c)

c) Either odd or even

16.

Whether it is true or false. Let a and b be positive integers such that a|b and b|a. Then a = b.

a)

a) False

b)

b) True

17.

Express 676 = ( )_eight.

a)

a) 1244

b)

b) 1145

c)

c)1028

18.

Find the number of ones in the binary representation of $2^5-1$

a)

a) 4

b)

b) 3

c)

c) 5

19.

Express (1101)₂ into octal integer.

a)

a) 15

b)

b) 17

c)

c)21

20.

Express 10110_two in base ten.

a)

a) 21

b)

b) 22

c)

c) 23

21.

Find the positive integer of 1976. It is divisible by 13

a)

a) 135

b)

b) 138

c)

c) 357

22.

Does the conjecture hold for $R_{10}^{2_{ }}$ ?

a)

a) Yes

b)

b) NO

23.

Using the formula of $\pi\left(n\right)$ find the number primes $\le100$

a)

a) 25

b)

b) 23

c)

c) 21

24.

Determine whether 129 is prime or composite

a)

a) Prime

b)

b)Prime and Composite

c)

c) Composite

25.

There are infinitely many primes

a)

a) Euclid

b)

b) Euler

c)

c) Prime

26.

Two positive integers a and b are relatively prime if their gcd is…….

a)

a) 2

b)

b) 1

c)

c) None of these

27.

Any two consecutive Fibonacci numbers are ….

a)

a) Common factor

b)

b) Relatively prime

c)

c) Fermat number

28.

In linear combination the values of $\alpha$ and $\beta$ is

a)

a) Unique

b)

b) Need not be unique

c)

c) None of these

29.

Find the number of trailing zeros in the decimal value of 1010!

a)

a) 251

b)

b) 241

c)

c) 231

30.

Find the positive integer a if [a,a+1]=132

a)

a) 12

b)

b) 11

c)

c) 11 or 12

ANT-IAT-II(MCQ)

Total questions: 30

Worksheet time: 30mins

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